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1. Squaring the Numbers By: Krishna Kumar Kumawat Maths Teacher

2. What is squaring? Squaring means that multiplying the term by itself.

3. Square of numbers whose unit digit is Zero ( 0 ) Just double the number of zeros at the right side and write the square of the non-zero number in left. Example 1: 40 2 = 1600 Example 2: 700 2 = 490000 Example 3: 2100 2 = 4410000 Example 4: 13000 2 = 169000000

4. Square of numbers whose unit digit is 5. Write 25 in the right most place, then. Multiply the rest number with its successive number and write in the left Example 1: 25 2 = 625 Example 2: 65 2 = 4225 Example 3: 85 2 = 7225 Example 4: 115 2 = 13225

5. Square of numbers whose unit digit is 1. Write the square of the previous number and then add the previous number and the number whose square is being asked Example 1: 21 2 = 20 2 + (20 + 21) = 400 + 41 = 441 Example 2: 81 2 = 80 2 + (80 + 81) = 6400 + 161 = 6561

6. Square of numbers whose unit digit is 9. It is very similar to the previous case. The difference is that here we have to subtract instead of addition. Example 1: 39 2 = 40 2 – ( 39 + 40 ) = 1600 - 79 = 1521 Example 2: 129 2 = 130 2 – ( 129 + 130 ) = 16900 - 259 = 16641

7. Square of numbers whose unit digit is 2. Write the square of the base number and then multiply the sum of the previous number and the number whose square is being asked, then add. Example 1: 52 2 = 50 2 + 2( 50 + 52) = 2500 + 204 = 2704 Example 2: 112 2 = 110 2 + 2( 110 + 112) = 12100 + 44 4 = 12544

8. Square of numbers whose unit digit is 8. Write the square of the base number and then multiply the sum of the base number and the number whose square is being asked by 2, then subtract it from the square of base number. Example 1: 38 2 = 40 2 - 2 ( 38 + 40 ) = 1600 - 156 = 1444 Example 1: 58 2 = 60 2 - 2 ( 58 + 60 ) = 3600 - 236 = 3364

9. Square of numbers whose unit digit is 3. Write the square of the base number and then multiply the sum of the base number and the number whose square is being asked by 3, then add it in the square of base number. Example 1: 23 2 = 20 2 + 3 ( 20 + 23 ) = 400 + 129 = 529 Example 1: 53 2 = 50 2 + 3 ( 50 + 53 ) = 2500 - 309 = 2809

10. Square of numbers whose unit digit is 7. Write the square of the base number and then multiply the sum of the base number and the number whose square is being asked by 3, then subtract it from the square of base number. Example 1: 47 2 = 50 2 - 3 ( 47 + 50 ) = 2500 - 291 = 2209 Example 1: 37 2 = 140 2 - 3 ( 137 + 140 ) = 19600 - 831 = 18769

11. Square of numbers whose unit digit is 4. Write the square of the base number and then subtract the sum of base number and the number whose square is being asked from the square of the base number. Example 1: 34 2 = 35 2 – ( 34+ 35 ) = 1225 - 69 = 1156 Example 2: 54 2 = 55 2 – ( 54 + 55 ) = 3025 - 109 = 2916

12. Square of numbers whose unit digit is 6. Write the square of the base number and then add the base number and the number whose square is being asked Example 1: 36 2 = 35 2 + (35+ 36) = 1225 + 71 = 1296 Example 2: 76 2 = 75 2 + (75 + 76) = 5625 + 151 = 5776

13. Important properties of squares 1. The numbers with unit digit 0 , 1, 5 or 6 always give the same unit digit respectively, on squaring . 2. If the unit digit of any number is 9 then the unit digit of the square of its number is always 1. 3. If the unit digit of any number is 2 or 8 then the unit digit of the square of its number is always 4.

14. Important properties of squares 4. If the unit digit of any number is 3 or 7then the unit digit of the square of its number is always 9. 5. If the unit digit of any number is 4 or 6 then the unit digit of the square of its number is always 6 . 6. 2, 3 7 and 8 never appear at unit digit in the square of a number.

15. Squaring the Numbers

16. Prepared by : Krishna Kumar Kumawat Maths Teacher C.F.D.A.V. Public School, Gadepan, Kota Rajasthan E-mail: kkk992840@yahoo.com Mob. 009928407883